a parabolic archway is 12 meters high at the vertex. at a height of 10 meters, the width of the archway is 8. how wide is the archway at ground level..
can somebody plz show me step by step to this, with the final answer at the end....thnx
2007-04-22 16:21:56 · 3 answers · asked by bb 4 in Science & Mathematics ➔ Mathematics
This parabola can be modeled by the equation y=ax^2+12. We just have to find out what a equals. When x=4, the height is 10, so solve this: 10=16a+12 or -2=16a or a=-1/8.
So the equation is y=(-1/8)x^2+12
2007-04-22 16:28:00 · answer #1 · answered by bruinfan 7 · 0⤊ 0⤋
We have an inverted parabola that can be described by the equation:
y = ax² + 12
We have three points on the parabola:
(0, 12); (-4, 10); and (4,10).
Plug in the third point and solve for a.
y = ax² + 12
10 = a(4²) + 12
-2 = 16a
a = -1/8
So the formula for the parabola is:
y = (-1/8)x² + 12
Now solve for x when y equals zero.
0 = (-1/8)x² + 12
x²/8 = 12
x² = 96
x = â96 = 4â6
The width of the archway at ground level is 2x.
2x = 2*4â6 = 8â6 â 19.595918
2007-04-24 12:06:00 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
omg i hate parabolas
2007-04-22 16:24:38 · answer #3 · answered by zsendukas 1 · 0⤊ 1⤋